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错设模型的极大似然估计AI 解读

This paper examines the consequences and detection of model misspecification when using maximum likelihood techniques for estimation and inference. The quasi-maximum likelihood estimator (QMLE) converges to a well defined limit, and may or may not be consistent for particular parameters of interest. Standard tests (Wald, Lagrange Multiplier, or Likelihood Ratio) are invalid in the presence of misspecification, but more general statistics are given which allow inferences to…

多项离散选择模型中分布错设下极大似然估计一致性的充分条件AI 解读

Paul A. Ruud, Sufficient Conditions for the Consistency of Maximum Likelihood Estimation Despite Misspecification of Distribution in Multinomial Discrete Choice Models, Econometrica, Vol. 51, No. 1 (Jan., 1983), pp. 225-228

一种常见缺失数据模式下回归系数估计量的小样本性质AI 解读

For a commonly occurring pattern of missing data, estimators of regression coefficients are derived by a non-likelihood method. The small-sample properties are investigated for the case of normality assumptions. The estimators are shown to be unbiased, exact small-sample variance formulae are derived, comparisons are made with ordinary least-squares estimators and it is demonstrated that the estimators can be more efficient than maximum-likelihood estimators in small samples.

多元时间序列模型中永久与暂时影响的分析AI 解读

Several multiple time series models are developed and applied to the analysis and forecasting of the M1 and M2 money supply aggregates. These models feature a decomposition of the time series into permanent and transient influences or components. This decomposition appears to enhance forecasting accuracy and is associated with a variance-covariance allocation parameter that is also estimated from the data. Conditional maximum likelihood estimates for model parameters are…

Logit生物测定中极端分位数的估计AI 解读

Suppose that we administer a low dose of a drug and if no response is observed, increase this dose by a fixed amount which is administered to a second experimental subject. This procedure continues until, at some dose level, a response is finally observed. This whole sequence may be repeated. We investigate the features of an experimental design of this kind for estimating the dose at which the expected response is small. This design is highly efficient when the number of…

平稳随机过程的 m 阶最大似然估计AI 解读

SUMMARY Sometimes the likelihood cannot be computed even introducing approximations whose effect is asymptotically negligible. To overcome this problem for inference from a stochastic process, we approximate the log likelihood by a sum whose generic term is the density function of the corresponding sample element conditional on the m most recent observations, for some m ≥ 0. General results on the asymptotic properties of the associated estimates are given, and numerical…

二元 Hermite 分布的若干估计方法AI 解读

Maximum likelihood estimation of bivariate Hermite parameters is awkward in that it requires iteration techniques which are complicated and relatively time-consuming even on modern computers. In the present paper we study several alternative estimation procedures which lead to explicit expressions for the parameter estimates in terms of fairly simple sample statistics. Asymptotic efficiencies are examined and recommendations made. For comparison, three simple methods are…

多元线性函数关系的估计AI 解读

Consistent estimation of the structural parameters in a multivariate linear functional relationship between two vector variables observed with error is considered. When the covariance matrix of the error terms contains unknown parameters, it is shown that the usual maximum likelihood approach generally yields inconsistent estimators. A natural modification of the likelihood equations leading to a consistent estimation procedure is proposed. The connexion with estimation in…

广义线性与非线性回归模型的极大似然估计及大样本推断AI 解读

The class of generalized linear models is extended to allow for correlated observations, nonlinear models and error distributions not of the exponential family form. The extended class of models include a number of important examples, particularly of the composite transformational type. Large-sample inference and maximum likelihood estimation for the extended class of generalized linear models are discussed, and the analysis of deviance is generalized to the extended class…

多元自回归指数模型的若干结果AI 解读

We discuss methods for modelling multivariate autoregressive time series in terms of a smaller number of index series which are chosen to provide as complete a summary as possible of the past information contained in the original series necessary for prediction purposes. The maximum likelihood method of estimation and asymptotic properties of estimators of the coefficients which determine the index variables, a well as the corresponding autoregressive coefficients, are…

高斯 ARMA 过程最大似然估计量的协方差矩阵计算AI 解读

We present a simple procedure for deriving the covariance matrix for the maximum likelihood estimator of a Gaussian autoregressive-moving average process. An illustration of the procedure is given.

通过几何规划估计多项分布概率的最大似然值AI 解读

SUMMARY This paper illustrates how the duality theory of geometric programming and the, special methods available for solution can be used to obtain maximum likelihood estimates for multinomial probabilities. Three examples are given.

空间模式的非参数最大似然估计AI 解读

Let $\mathbf{X}$ be an absolutely continuous random variable in $\mathbb{R}^k$ with distribution function $F(\mathbf{x})$ and density $f(\mathbf{x})$. Let $\mathbf{X}_1, \cdots, \mathbf{X}_n$ be independent random variables distributed according to $F$. Mapping the spatial distribution of $\mathbf{X}$ normally entails drawing a map of the isopleths, or level curves, of $f$. In this paper, it is shown how to map the isopleths of $f$ nonparametrically according to the…

含Box–Cox变换模型参数估计的快速高效算法AI 解读

A modified Newton algorithm for the estimation of parameters in models containing the Box-Cox transformation is presented. It is shown that the usual maximum likelihood estimator for the k linear parameters and the m power transformation parameters may be specified as an m-parameter nonlinear least squares estimator. Several models containing Box-Cox transformations are estimated and the speed and efficiency of the modified algorithm compared with three other gradient…

异方差线性模型中最大似然与广义最小二乘的比较AI 解读

We consider a linear model with normally distributed but heteroscedastic errors. When the error variances are functionally related to the regression parameter, one can use either maximum likelihood or generalized least squares to estimate the regression parameter. We show that likelihood is more sensitive to small misspecifications in the functional relationship between the error variances and the regression parameter.

一个不一致的最大似然估计AI 解读

An example is given of a family of distributions on [— 1, 1] with a continuous one-dimensional parameterization that joins the triangular distribution (when Θ = 0) to the uniform (when Θ = 1), for which the maximum likelihood estimates exist and converge strongly to Θ = 1 as the sample size tends to infinity, whatever be the true value of the parameter. A modification that satisfies Cramér's conditions is also given.

非线性学习模型的估计AI 解读

The article develops the structure and estimates the parameters of a nonlinear learning model applicable to research designs in which students are tested at the beginning and end of a course of study. A student's precourse score is an error-ridden proxy for his precourse aptitude. As a remedy for this problem, the article combines a probit model of test score outcomes, a learning function, and a linear equation relating aptitude to demographic characteristics to deduce the…

基于最大似然的循环配对方差分析AI 解读

A class of two-way random-effects models is presented for analyzing data that arise in a large variety of round robin designs. Examples of such designs can be found in numerous games, tournaments, and social interactions. The proposed models provide information not only about individual differences but also about the mutual contingency of the behaviors of interaction dyads. The statistical inference of the linear effects is discussed and a converging algorithm based on the…

一个不一致的最大似然估计AI 解读

An example is given of a family of distributions on [— 1, 1] with a continuous one-dimensional parameterization that joins the triangular distribution (when Θ = 0) to the uniform (when Θ = 1), for which the maximum likelihood estimates exist and converge strongly to Θ = 1 as the sample size tends to infinity, whatever be the true value of the parameter. A modification that satisfies Cramér's conditions is also given.

非线性学习模型的估计AI 解读

The article develops the structure and estimates the parameters of a nonlinear learning model applicable to research designs in which students are tested at the beginning and end of a course of study. A student's precourse score is an error-ridden proxy for his precourse aptitude. As a remedy for this problem, the article combines a probit model of test score outcomes, a learning function, and a linear equation relating aptitude to demographic characteristics to deduce the…

基于最大似然的循环配对设计方差分析AI 解读

A class of two-way random-effects models is presented for analyzing data that arise in a large variety of round robin designs. Examples of such designs can be found in numerous games, tournaments, and social interactions. The proposed models provide information not only about individual differences but also about the mutual contingency of the behaviors of interaction dyads. The statistical inference of the linear effects is discussed and a converging algorithm based on the…

用 EM 算法求解结构化协方差矩阵的最大似然估计AI 解读

Some patterned covariance matrices used to model multivariate normal data that do not have explicit maximum likelihood estimates can be viewed as submatrices of larger patterned covariance matrices that do have explicit maximum likelihood estimates. In such cases, the smaller covariance matrix can be viewed as the covariance matrix for observed variables and the larger covariance matrix can be viewed as the covariance matrix for both observed and missing variables. The…

混合双随机泊松与自激点过程的线性强度模型AI 解读

Summary A flexible family of parametric models for intensity processes is introduced to represent a causal relationship between a point process and another stochastic process. Algorithms for the maximum likelihood computation and the procedure of model selection are discussed.

斜率系数最大似然估计量的精确分布与近似分布AI 解读

Summary When the errors are normally independently distributed with equal variance, the maximum likelihood estimator of the slope of a linear functional relationship is the slope of the line minimizing the sum of squared deviations orthogonal to the line. The exact density and distribution of this estimator are obtained. Approximate distributions are obtained, and their accuracies are discussed.